Multiple choice

In a small village, a historian is researching the ages of key individuals in an old family lineage to complete a historical record. John is 31 years older than Emily, Emily is 3 years older than Sarah, and Michael is 5 years younger than Sarah. Three years from now, John's age will be equal to the combined ages of Emily, Sarah, and Michael. Determine the present age of John to help the historian complete the record.

  1. 43

  2. 46

  3. 49

  4. 52
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let Sarah's age be S. Emily = S+3, John = S+3+31 = S+34, Michael = S-5. Three years from now: John+3 = (Emily+3) + (Sarah+3) + (Michael+3). (S+34+3) = (S+3+3) + (S+3) + (S-5+3). S+37 = 3S+7. 2S = 30, S = 15. John = 15+34 = 49.

AI explanation

Let John's age be J, Emily's be E, Sarah's be S, and Michael's be M. The problem provides the equations J = E + 31, E = S + 3, and M = S - 5. The condition for three years from now is J + 3 = (E + 3) + (S + 3) + (M + 3), which simplifies to J = E + S + M + 6. Substituting the first three equations into this gives S + 34 = (S + 3) + S + (S - 5) + 6, which simplifies to S + 34 = 3S + 4. Solving for S gives S = 15, and since J = S + 34, John's present age is 49 years.

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